Abstract
We propose a dynamic programming approach to address the problem of determining how a structured formation of autonomous undistinguishable agents can be reorganized into another, eventually non-rigid, formation based on changes in the environment, perhaps unforeseeable. The methodology can also be used to correctly position the agents into a particular formation from an initial set of random locations. Given the information of the current agents location and the final locations, there are n! possible permutations for the n agents, and we seek the one that minimizes a total relative measure, e.g. distance traveled by the agents during the switching. Possible applications can be found amongst surveillance, damage assessment, chemical or biological monitoring, among others. where the switching to another formation, not necessarily predefined, may be required due to changes in the environment.

Abstract
We exploit ideas of nonlinear dynamics in a non-deterministic dynamical setting. Our object of study is the observed riverflow time series of the Portuguese Paiva river whose water is used for public supply. The Takens delay embedding of the daily riverflow time series revealed an intermittent dynamical behaviour due to precipitation occurrence. The laminar phase occurs in the absence of rainfall. The nearest neighbour method of prediction revealed good predictability in the laminar regime but we warn that this method is misleading in the presence of rain. The correlation integral curve analysis, Singular Value Decomposition and the Nearest Neighbour Method indicate that the laminar regime of flow is in a small neighbourhood of a one-dimensional affine subspace in the phase space. The Nearest Neighbour method attested also that in the laminar phase and for a data set of 53 years the information of the current runoff is by far the most relevant information to predict future runoff. However the information of the past two runoffs is important to correct non-linear effects of the riverflow as the MSE and MRE criteria results show. The results point out that the Nearest Neighbours method fails when used in the irregular phase because it does not predict precipitation occurrence. © 2007, Birkhäuser Verlag Basel/Switzerland.

Abstract
There is a one-to-one correspondence between C 1+H Cantor exchange systems that are C 1+H fixed points of renormalization and C 1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor ? that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on ?. However, there is no such C 1+a Cantor exchange system with bounded geometry that is a C 1+a fixed point of renormalization with regularity a greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor ? are not C 1+? for ? greater than the Hausdorff dimension of the stable leaves of f intersected with ?. © 2007, Birkhäuser Verlag Basel/Switzerland.

Abstract
We consider a Bertrand duopoly model with unknown costs. The firms' aim is to choose the price of its product according to the well-known concept of Bayesian Nash equilibrium. The chooses are made simultaneously by both firms. In this paper, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We analyse the advantages, for firms and for consumers, of using the technology with highest production cost versus the one with cheapest production cost. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.

Abstract
The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We demonstrate that cytokine dependent growth exhibits quorum T cell population thresholds that determine whether immune responses develop on activation and whether the immune system returns to a control state. We study the effects in the quorum T cell population thresholds, by the T cell maximum growth rate, by the growth rate ratio between Tregs and T cells, by the value of the secretion rate of cytokines, and by the effectiveness of T cell secretion inhibition by Tregs.

Abstract
In this paper, we consider a Stackelberg duopoly competition with differentiated goods and with unknown costs. The firms' aim is to choose the output levels of their products according to the well-known concept of perfect Bayesian equilibrium. There is a firm (F(1)) that chooses first the quantity q(1) of its good; the other firm (F(2)) observes q(1) and then chooses the quantity g(2) of its good. We suppose that each firm has two different technologies, and uses one of them following a probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the advantages, for firms and for consumers, of using the technology with the highest production cost versus the one with the cheapest cost.